Which explicit rule is correct for the sequence (5,7,11,19,\ldots)?
Answer and explanation
Correct answer: \(a_n=2^n+3\)
Here the terms are counted from \(n=1\). Substituting \(n=1,2,3,4\) in \(a_n=2^n+3\) gives \(5,7,11,19\), respectively, so it is the correct explicit rule. \(a_n=2n+3\) matches only the first two terms; for the third term it gives \(9\), not \(11\). Exam tip: test an explicit rule using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=2^n+3\)
Why is this the correct answer?
Here the terms are counted from \(n=1\). Substituting \(n=1,2,3,4\) in \(a_n=2^n+3\) gives \(5,7,11,19\), respectively, so it is the correct explicit rule. \(a_n=2n+3\) matches only the first two terms; for the third term it gives \(9\), not \(11\). Exam tip: test an explicit rule using at least the first three values of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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